Two insulated long, straight wires cross each other at right angle, and each car

Question

Two insulated long, straight wires cross each other at right angle, and each carries the same current I. Which of the following statements is true regarding the total magnetic field due to the two wires at the various points in the figure below? All points arc equal distance to the wires. More than one statement may be correct. The field is strongest at points B and D. The field is strongest at points A and C. The field is out of the page at point C and into the page at point A. The field is out of the page at point B and out of the page at point D. The field has the same magnitude at all four points. Describe the magnetic force each apply to one another.

Explanation / Answer

i)

For point A,

By right hand rule of magnetic field, direction magnetic field by vertical current wire is into the page and by horizontal current wire is also into the page.

Hence

Bnet= B1+ B2

For point C,

By right hand rule of magnetic field, direction magnetic field by vertical current wire is out of the page and by horizontal current wire is also out of the page.

Hence

Bnet= B1+ B2 = 2B

For point B,

For point B,

By right hand rule of magnetic field, direction magnetic field by vertical current wire is out of the page and by horizontal current wire is into the page.

Hence

Bnet= B1- B2 = 0 unit

For point D,

By right hand rule of magnetic field, direction magnetic field by vertical current wire is into the page and by horizontal current wire is out of the page.

Hence

Bnet= B1- B2 = 0 unit

Thus correct answers are:

a) point A and C have strongest B.

c) The field is into the page for point A and out of the page for point A

ii) For magnetic force use equation,

F= L(I x B) = LIB

So at point B and D magnetic force = 0 unit

For point A,

Magnetic force on horizontal wire is directed downward.

Magnetic force on vertical wire is directed left.

For point C,

Magnetic force on horizontal wire is directed to upward.

Magnetic force on vertical wire is directed to the right.

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